What is the value of 2 sin 75° cos 75° ?

  1. \(\frac 12\)
  2. \(\frac 1 {\sqrt 2}\)
  3. \(\frac {\sqrt 3}2\)
  4. None of these

Answer (Detailed Solution Below)

Option 1 : \(\frac 12\)
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Detailed Solution

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Concept:

2sinx cos x = sin 2x

sin (90° + x) = cos x

Calculation:

Given, 2 sin 75° cos 75°

= sin [2 (75°)]

= sin (150°)

= sin (90° + 60°)

= cos 60°

\(\rm \dfrac 1 2\)

Hence, the value of 2 sin 75° cos 75° is \(\rm \dfrac 1 2\)

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